Author 
Message 
silicon2006@hotmail.com science forum beginner
Joined: 19 May 2006
Posts: 6

Posted: Thu Jun 15, 2006 8:37 am Post subject:
a question related to mutivariable normal distribution



(1) If x1, x2, x3, ..., xn all follow the same normal distribution (a,
sigma),
does x=maximum(x1, x2, ..., xn) also follow normal distribution?
(2) If x=maximum(x1, x2, ..., xn) does follow normal distribution,
what is mean(x) and std(x)? 

Back to top 


john2 science forum beginner
Joined: 01 Feb 2006
Posts: 15

Posted: Thu Jun 15, 2006 1:08 pm Post subject:
Re: a question related to mutivariable normal distribution



silicon2006@hotmail.com wrote:
Quote:  (1) If x1, x2, x3, ..., xn all follow the same normal distribution (a,
sigma),
does x=maximum(x1, x2, ..., xn) also follow normal distribution?
(2) If x=maximum(x1, x2, ..., xn) does follow normal distribution,
what is mean(x) and std(x)?

A rank statistics problem [qv]. If x1..xn are independent, the CDF of
the largest sample is the nth power of the CDF of a single sample and
the PDF is not normal, though it might approximate it.
john2 

Back to top 


Debashis Dash science forum beginner
Joined: 16 Jun 2006
Posts: 1

Posted: Fri Jun 16, 2006 12:00 am Post subject:
Re: a question related to mutivariable normal distribution



It is true that the distribution is not normal (gaussian to be more
general), but you can easilly find its CDF and PDF:
(capital F is the CDF and f is the pdf and subscript denotes the variable)
Let Y=max(X_1, X_2, ..., X_N)
Then, F_Y(a)=Pr(Y<=a)
=Pr(max(X_1, X_2, ..., X_N)<=a)
=Pr(X_1<=a).Pr(X_2<=a)...Pr(X_N<=a)
={F_X(a)}^N
Hence, f_Y(a)=d/da(F_Y(a))=N(F_X(a))^(N1).f_X(a)
Which is not a surprise.
DD
"john2" <john2@8889.fsnet.co.uk> wrote in message
news:e6rm4n$c7g$1@newsg4.svr.pol.co.uk...
Quote:  silicon2006@hotmail.com wrote:
(1) If x1, x2, x3, ..., xn all follow the same normal distribution (a,
sigma),
does x=maximum(x1, x2, ..., xn) also follow normal distribution?
(2) If x=maximum(x1, x2, ..., xn) does follow normal distribution,
what is mean(x) and std(x)?
A rank statistics problem [qv]. If x1..xn are independent, the CDF of the
largest sample is the nth power of the CDF of a single sample and the PDF
is not normal, though it might approximate it.
john2 


Back to top 


Ray Koopman science forum Guru Wannabe
Joined: 25 Mar 2005
Posts: 216

Posted: Fri Jun 16, 2006 7:48 am Post subject:
Re: a question related to mutivariable normal distribution



Debashis Dash wrote:
Quote:  ,,,the distribution is not normal (gaussian to be more general)...

How do you see "gaussian" as more general than "normal"? 

Back to top 


Google


Back to top 



The time now is Fri Sep 21, 2018 3:24 pm  All times are GMT

